Related papers: Dispersive shallow water wave modelling. Part II: …
A weakly magnetized neutron star (NS) undergoing disk accretion should release about a half of its power in a compact region known as the accretion boundary layer. Latitudinal spread of the accreted matter and efficient radiative cooling…
We are interested in asymptotic models for the propagation of internal waves at the interface between two shallow layers of immiscible fluid, under the rigid-lid assumption. We review and complete existing works in the literature, in order…
We consider the Serre system of equations which is a nonlinear dispersive system that models two-way propagation of long waves of not necessarily small amplitude on the surface of an ideal fluid in a channel. We discretize in space the…
The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a…
Cartesian-grid methods in combination with immersed-body and volume-of-fluid methods are ideally suited for simulating breaking waves around ships. A surface panelization of the ship hull is used as input to impose body-boundary conditions…
In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the…
A non-negativity-preserving cut-cell discontinuous Galerkin method for the degenerate parabolic diffusive wave approximation of the shallow water equation is presented. The method can handle continuous and discontinuous bathymmetry as well…
We present a spectral element model for general-purpose simulation of non-overturning nonlinear water waves using the incompressible Navier-Stokes equations (INSE) with a free surface. The numerical implementation of the spectral element…
This paper focuses on the numerical approximation of the linearized shallow water equations using hybridizable discontinuous Galerkin (HDG) methods, leveraging the Hamiltonian structure of the evolution system. First, we propose an…
We introduce a new class of Green-Naghdi type models for the propagation of internal waves between two (1+1)-dimensional layers of homogeneous, immiscible, ideal, incompressible, irrotational fluids, vertically delimited by a flat bottom…
We develop a general approach to the description of dispersive shock waves (DSWs) for a class of nonlinear wave equations with a nonlocal Benjamin-Ono type dispersion term involving the Hilbert transform. Integrability of the governing…
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly…
We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main…
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
Heterogeneous computing and exploiting integrated CPU-GPU architectures has become a clear current trend since the flattening of Moore's Law. In this work, we propose a numerical and algorithmic re-design of a p-adaptive quadrature-free…
When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we…
We consider linear and nonlinear hyperbolic SPDEs with mixed derivatives with additive space-time Gaussian white noise of the form $Y_{xt}=F(Y) + \sigma W_{xt}.$ Such equations, which transform to linear and nonlinear wave equations,…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible…